Enter Coefficients
Use integer coefficients for a quadratic in the form ax2 + bx + c.
Example Data Table
| a | b | c | a × c | Split Pair | Factored Form |
|---|---|---|---|---|---|
| 1 | 5 | 6 | 6 | (2, 3) | (x + 2)(x + 3) |
| 2 | 7 | 3 | 6 | (1, 6) | (2x + 1)(x + 3) |
| 3 | -11 | -4 | -12 | (1, -12) | (3x + 1)(x - 4) |
| 1 | 2 | 5 | 5 | No integer pair | Not factorable over the integers |
Formula Used
The X method works on a trinomial written as ax² + bx + c.
- Multiply the leading coefficient and constant term: a × c.
- Find integers m and n such that m × n = a × c.
- Those same integers must also satisfy m + n = b.
- Rewrite the middle term as mx + nx, then factor by grouping.
How to Use This Calculator
- Enter integer values for coefficients a, b, and c.
- Optionally change the variable symbol and choose whether to show steps and graph.
- Press Calculate to see the factorization above the form.
- Review the split pair, discriminant, roots, and grouped form.
- Use the CSV or PDF buttons to save the current result.
FAQs
1. What does the X method do?
It helps factor quadratic trinomials by multiplying a and c, then finding two integers that match the needed product and middle-term sum.
2. Does this calculator work for any quadratic?
It works best when the trinomial factors over the integers. If no suitable integer pair exists, the calculator reports that the expression is not factorable over the integers.
3. Why must a be nonzero?
A nonzero a makes the expression quadratic. If a equals zero, the expression becomes linear, so the X method no longer applies.
4. Why does the calculator show a × c first?
That product is the center of the X method. It determines which integer pair you must search for before splitting the middle term.
5. What if the constant term is zero?
Then the trinomial has an immediate common factor of the variable. The calculator factors that case directly before showing the remaining linear factor.
6. Why are roots included?
Roots help you verify the factorization. When the factors are correct, the graph crosses the x-axis at those root values whenever the roots are real.
7. Can I use negative coefficients?
Yes. The calculator handles negative values, extracts a common factor when useful, and then applies the X method to the reduced trinomial.
8. What do the CSV and PDF buttons save?
They save the current result summary, including coefficients, product, split pair, roots, and factored form. This is useful for homework review or record keeping.